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Dissertation Critique

Dissertation Critique. Gwenanne Salkind George Mason University December 8, 2007 EDCI 858 & EDCI 726 Dr. Patricia Moyer-Packenham Dr. Margret Hjalmarson. Examining the Work of Constructing a Representational Context in Elementary Mathematics Teaching. By Rhonda B. Cohen

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Dissertation Critique

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  1. Dissertation Critique Gwenanne Salkind George Mason University December 8, 2007 EDCI 858 & EDCI 726 Dr. Patricia Moyer-Packenham Dr. Margret Hjalmarson

  2. Examining the Work of Constructing a Representational Context in Elementary Mathematics Teaching By Rhonda B. Cohen University of Michigan Doctoral Committee: Professor Deborah Loewenberg Ball, Chair Professor Hyman Bass Professor Magdalene Lampert Professor Elizabeth Yakel

  3. Research Questions • What is the work of constructing a representational context in elementary mathematics teaching? • How does studying the work of constructing a representational context make more visible what teachers need to know and be able to do to use these kinds of instructional representations effectively in elementary mathematics teaching?

  4. Central Questions • What might teachers need to know in order to help students develop meaning for a representation? • What might teachers need to be able to do to help students learn to use a representation? • What might be some of the challenges or dilemmas in this work?

  5. Methods • Data Sources: Records of teaching (videotaped lessons, lesson transcripts, copies of student work, and teachers’ notes) of a third grade mathematics class taught by Deborah Ball during the 1989-90 school year. • Qualitative Case Study: Analyzed 3 teaching episodes where Ball introduced a representation to help students solve a mathematics problem.

  6. Theoretical Foundation of Analysis • Mathematical Knowledge for Teaching • Common content knowledge • Specialized content knowledge • Knowledge of content and students • Knowledge of content and teaching

  7. Representations • Square Tiles – How does the teacher establish the language needed to deploy a representation? • Elevator Model – How does the teacher make a representation usable to students? • Number Line - What does the teacher do to make connections to other representations (especially representations that students introduce)?

  8. Results • The work of launching and preparing to use a representation involves knowing mathematics in ways that are special to the work of teaching. • Demand for mathematical knowledge, skill, and sensibilities • Need to be judicious in how language and mathematical symbols get used • Importance of attending to the ways in which students’ prior knowledge and experience can both support and hinder the work of constructing a representational context

  9. Establishing the Language • Helping students record mathematical ideas in ways that emphasize the correspondences among the words, symbols, and materials • Attending closely to the meaning of mathematical terms and the use of language • Using transitional language • Noticing the mathematical ideas for which a representation can be used and relating those ideas to what students need to learn

  10. Making Representation Usable • Attending closely to the meaning of the mathematical symbols and the use of language • Piquing students’ interest • Drawing students’ attention to key features and teaches students how to use the representation • Comparing the relative merits of different representations

  11. Making Connections • Attending closely to what students mean by the terms “same” and “different” • Drawing students’ attention to a structural elements that need to be the same for different representations • Helping students give explanations • Attending to task design considerations

  12. Teaching Challenges • Establishing the language needed to deploy a representation • Making a representation usable for students • Making connections to other representations

  13. Ideas for Teacher Education • Help teachers attend closely to how recording work with mathematical tools (e.g., base-ten blocks) can be used to emphasize the mathematics content being studied • Have teachers explain the correspondences between a representation and the mathematics content

  14. Ideas for Teacher Education • Use caution in emphasizing the motivational purposes for using representations in teaching mathematics • Help teachers develop criteria for discriminating among representations used in mathematics teacher – compare the relative merits of different representations

  15. Critique • Redundancy • Focus • Organization & Structure • Omit the section on “Designing Introductory Tasks”

  16. Questions I have • Does this study generalize to other teachers’ work? • If she had studied a different teacher, would she have found the same results?

  17. Key Components – things I learned • Her acknowledgement page was eloquently written • She identified themes in her literature review • Her argument for the study was both broad and specific – approached from many angles • She defined terms and assumptions (tons of this!) • She described her perspectives (lenses) • She tells what she is doing and why she is doing it (over and over again!) • She used stories and vignettes as examples and illustrations of her analyses

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